The three body problem is reviewed. Euler and Lagrange found collinear and equilateral triangular solutions, respectively. However, attempts for searching a general solution for the three body problem finished soon after Poincare discovered chaotic behaviors in the restricted three body problem. In the general relativistic gravity, the three body problem is revisited. The post-Newtonian counterparts of the collinear and triangular solutions are obtained. The relativistic hierarchical triple system including a millisecond pulsar J0337+1715 allows a direct test of the strong equivalence principle. Moreover, a possible relevance of the three body system to gravitational wave astronomy is also mentioned.
Structural quantum phase transitions have received less attention thus far than magnetic quantum phases and remain an unexplored research field in materials science. Here, we report the nature of two structural quantum materials, Ba1-x Srx Al2O4 and(Sr1-x Cax)3Rh4Sn13 . Both compounds show structural phase transitions for which acoustic-type soft modes are responsible, and the structural quantum critical points (sQCPs) appear by chemical substitution. Using synchrotron x-ray diffraction, pair distribution function analysis, and inelastic neutron scattering, we demonstrate that a glasslike atomic network is realized at the sQCP of Ba1-x Srx Al2O4 . This glassy state dampens all phonons in the whole energy range, resulting in the excess lattice-specific heat at low temperatures. Similar excess in the lattice-specific heat is also observed for (Sr1-x Cax)3Rh4Sn13 . We believe that the glassy phonon properties should be the essential nature of the sQCP associated with the soft acoustic mode.
Substituting cobalt for iron in perovskite bismuth ferrite changes its spin structure from cycloid to collinear and induces canted spin spontaneous magnetization perpendicular to the electric polarization. Magnetization reversal by electric field was demonstrated in thin films on GdScO3 substrates by observing ferroelectric and magnetic domains at the same area. The different manner of magnetization reversal depending on the poling direction is also discussed. This characteristic is expected to be utilized as an ultra-low-energy-consuming non-volatile magnetic memory device that enables writing information by electric field.